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Proof step 110 from proof abs-nodes-add-crash-aligned-h (previous step)

# buf3 = NODE_HEADER_SIZE, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf4 = a0.alignedsize + 2 * NODE_HEADER_SIZE, subarray(buf3 + buf0 + validtrailer, 0, n) = buf4 + buf2, n < 2 * NODE_HEADER_SIZE + # buf0, n < 2 * NODE_HEADER_SIZE + # buf0 + # buf + # buf1, abs-node(buf4, a0), abs-node(buf1, a), abs-nodes(buf2, m + # buf4, x0 + a ', lax0 + @(2 * NODE_HEADER_SIZE + m + # buf0 + # buf, # buf1) ', boolvar), abs-nodes(buf, 2 * NODE_HEADER_SIZE + m + # buf0, a0 ' + x0, @(m, # buf4) ' + lax0, false), is-aligned(n, NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), is-aligned(# buf0, 2 * NODE_HEADER_SIZE), is-encoded(nodeheader(# buf0, true), buf3), ∀ buf4, buf1, a, n, m, x, lax, boolvar. # buf4 < #((buf3 + buf0 + validtrailer) + buf) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf4 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf4 + buf1, 0, n), m, x + a ', lax + @(m + # buf4, # buf1) ', boolvar) ∧ abs-nodes(buf4, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf4 + # buf1 ⊦ buf3 + buf0 + validtrailer = mkbuf(0), n = 2 * NODE_HEADER_SIZE + # buf0 + # buf + # buf1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 111:
⊦ abs-node(buf, nd) ↔ (∃ buf0, buf1. buf = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(nd), false), buf0) ∧ is-encoded(nd, subarray(buf1, 0, node-size-headerless(nd))) ∧ # buf1 = nd.alignedsize)
Proof step 112:
# buf4 = a0.alignedsize + 2 * NODE_HEADER_SIZE, # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE, # buf3 = NODE_HEADER_SIZE, subarray(buf3 + buf0 + validtrailer, 0, n) = buf4 + buf2, n < 2 * NODE_HEADER_SIZE + # buf0 + # buf + # buf1, n < 2 * NODE_HEADER_SIZE + # buf0, abs-node(buf1, a), abs-nodes(buf, 2 * NODE_HEADER_SIZE + m + # buf0, a0 ' + x0, @(m, # buf4) ' + lax0, false), abs-nodes(buf2, m + # buf4, x0 + a ', lax0 + @(2 * NODE_HEADER_SIZE + m + # buf0 + # buf, # buf1) ', boolvar), is-aligned(# buf0, 2 * NODE_HEADER_SIZE), is-aligned(m, NODE_HEADER_SIZE), is-aligned(n, NODE_HEADER_SIZE), is-encoded(nodeheader(# buf0, true), buf3), ∃ buf0, buf1. buf4 = buf0 + buf1 + validtrailer ∧ is-encoded(nodeheader(node-size-headerless(a0), false), buf0) ∧ is-encoded(a0, subarray(buf1, 0, node-size-headerless(a0))) ∧ # buf1 = a0.alignedsize, ∀ buf4, buf1, a, n, m, x, lax, boolvar. # buf4 < #((buf3 + buf0 + validtrailer) + buf) → # buf1 = a.alignedsize + 2 * NODE_HEADER_SIZE ∧ n < # buf4 + # buf1 ∧ abs-node(buf1, a) ∧ abs-nodes(subarray(buf4 + buf1, 0, n), m, x + a ', lax + @(m + # buf4, # buf1) ', boolvar) ∧ abs-nodes(buf4, m, x, lax, false) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ is-aligned(m, NODE_HEADER_SIZE) → n = # buf4 + # buf1 ⊦ buf3 + buf0 + validtrailer = mkbuf(0), n = 2 * NODE_HEADER_SIZE + # buf0 + # buf + # buf1

Rule argument

spec: abs-node name: abs-node seq: ⊦ abs-node(buf, nd) ↔ (∃ buf0, buf1. buf = buf0 + buf1 + validtrailer ∧ is-encoded (nodeheader(node-size-headerless(nd), false), buf0) ∧ is-encoded (nd, subarray(buf1, 0, node-size-headerless(nd))) ∧ # buf1 = nd.alignedsize) subst: [nd, buf] → [a0, buf4] flags: <all paths>

Additional information

Used terms: a0, buf4